Pand Q are the points on the sides ABand AC of a triangle ABC such that AP = 3 cm, AB = 6 cm, AQ = 7 cm and AC= 21 cm. Is PO||BC? Give reasons for your answer.
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Pand Q are the points on the sides ABand AC of a triangle ABC such that AP = 3 cm, AB = 6 cm, AQ = 7 cm and AC= 21 cm. Is PO||BC? Give reasons for your answer.
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Step-by-step explanation:
We have
(
AC
AQ
)=
9
3
=
3
1
(
AB
AP
)=
10.5
3.5
=
3
1
In ΔAPQ & ΔABC
(
AC
AQ
)=(
AB
AP
)
& ∠PAQ=∠BAC
Thus ΔAPQ∼ΔABC by SAS criterion.
Hence (
AC
AQ
)=(
BC
PQ
) (by cpst)
⇒
3
1
=(
BC
4.5
)
⇒BC=13.5cm.
Answer:
In triangle ABC, P and Q are points on sides AB and AC respectively such that P Q ∣ ∣ B C . Hence, the value of BC is 7.5 cm.
Step-by-step explanation: